## 385 Reputation

6 years, 287 days

## I still need you...

I want to trace the tangent in P to p

a := 7;
b := 3;
t := (2*Pi)/3;
NULL;
ellipse(p, x^2/a^2 + y^2/b^2 - 1, [x, y]);
point(P, a*cos(t), b*sin(t));
NULL;
rotation(q, p, t, 'clockwise', P);
tangentpc(Tg, P, p);
Error, (in geometry:-tangentpc) wrong type of arguments

draw([p(color = blue), P, q(color = blue),Tg(color=red), axes = normal, scaling = constrained);
Why this error message.? Thank you.

## More efficient procedure...

how to highlight that the sum of the sides is constant ? Thank you.
Fig := proc(t)
local xD,yD, D, C,Points,tex;
global A, B, b, Omega1, EL1, EL2;
xD:=Omega1[1]+aa*cos(t):
yD:=bb*sin(t):
D:= [xD, yD]; C := [xD + b, yD];
Points := pointplot([A[], B[], C[], C[], D[], E[], Omega1[]], symbol = solidcircle, color = [red],     symbolsize = 6):
tex := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"], [E[], "E"], [Omega1[], "&Omega;1"]], align = ["above", "right"]):
display([polygonplot([A, B, C, D], color = blue, filled = true, transparency = 0.9), Points,tex,EL1, EL2], axes = normal, scaling = constrained);
end proc:
Fig((3*Pi)/4);
display([seq(Fig((2*Pi*i)/40), i = 1 .. 80)], insequence = true):

## Too small drawing...

I still have a problem
restart:
with(plots):
with(plottools):
_EnvHorizontalName:= 'x':
_EnvVerticalName:= 'y':
EqBIS:= proc(P, U, V)
local a, eq, eq1, M1, t, PU, PV, bissec1:
uses geometry, LinearAlgebra:
description "P est le sommet de l'angle dont on chercche la bissectrice" :
a:= (P - U)/Norm(P - U, 2) + (P - V)/Norm(P - V, 2):
M1:= P + a*t:
eq1:= op(eliminate({x = M1[1], y = M1[2]}, t)):
eq:= op(eq1[2]):
line(bis, eq):
line(lv, x = 2*sqrt(r1*R)):
intersection(Omega, bis, lv):
return coordinates(Omega);
end proc:
r1:= 1/2:
r2:= r1/2:
R:= r1*(21 - 12*sqrt(3)):
R:= r1*(21 - 12*sqrt(3)):
a:= arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6):
b:= arc([0, 0], r1, Pi/6 .. (5*Pi)/6):
co:= EqBIS(<sqrt(3)/2, 1/2>, <0, 0>, <0, 1/2>):
A:=[cos(Pi/6), sin(Pi/6)]:
B:=[cos(5*Pi/6), sin(5*Pi/6)]:
Oo:=[0,0]:
Op:=[0,1/2]:
poly:=[A,B,Oo]:
Omega:= [co[1], co[2]]:
Omega1:= [-co[1], co[2]]:
r3:= 3/16:
EF:= sqrt(r3):
r:= (150 - 72*sqrt(3))/193*1/2:
alpha:= -5/3*r + 1/2*1/2:
p:= sqrt(3)/3*1/2 - sqrt(3)/18*r:
p2:= textplot([[A[], "A"], [B[], "B"], [Oo[], "O"]], align = ["above", "right"]):
display( [ a,
b,
seq(plot([[1/2*cos(Pi/6+i*1/5), 1/2*sin(Pi/6+i*1/5)],[0,0]],i=1..10),color=black),
sector([0,0], 1/2, Pi/6.. 5*Pi/6, color =white,transparency=0.3),
polygonplot(poly, thickness = 3, color = blue,transparency=0.7),
disk(Omega, R, color = blue),
disk(Omega1, R, color = blue),
disk([0, 3/4], 1/4, color = yellow),
disk([EF, 1/2 + r3], r3, color = green), disk([-EF, 1/2 + r3], r3, color = green),
circle([-EF, 1/2 + r3], r3, color = black),
circle([p, 3/4 + alpha], r, color = black),disk([p, 3/4 + alpha], r, color = red),
circle([-p, 3/4 + alpha], r, color = black),disk([-p, 3/4 + alpha], r, color = red)
],
axes = none,
scaling = constrained,
size = [500, 500]
);
Warning, data could not be converted to float Matrix, I don't understand this message. Thank you for your help.

## an ellipse between 2 circles and 2 commo...

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 11:
r := 7:
a := sqrt(R*r):

b := 2:
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [R + 2*b + r, 0]), r]):
ellipse(p, (x - R - b)^2/b^2 + y^2/a^2 = 1):
draw([C1(color = yellow, filled = true),
C2(color = red, filled = true), p(color = blue, filled = true),
C1(color = black), C2(color = black), p(color = black)],
axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained):
alpha := arctan((R - r)/(R + 2*b + r));
long := cos(alpha)*(R + 2*b + r);
evalf(%);
circle(C2, [point(P2, [long, r - R]), r]);
rotation(p1, p, alpha, 'clockwise');
detail(p1);
point(A, 0, -R);
point(B, long, -R);
line(L1, [A, B]);
point(cen, [(143*sqrt(5))/25, -(26*sqrt(5))/25]);
line(L, [P1, P2]);
reflection(L2, L1, L);
detail(L2);
draw([C1(color = yellow, filled = true), C2(color = red, filled = true), p1(color = blue, filled = true), C1(color = black), C2(color = black), p1(color = black), L1(color = black), L2(color = black)], axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained);
The drawing is a sangatku.

## Other difficulty wirth the circle C5 ; ...

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 7:
point(A, [0, R]):
line(L1, y = sqrt(3)*x + R):
line(L2, y = -sqrt(3)*x + R):
line(L3, y = R/3):
intersection(B, L1, L3):
intersection(C, L2, L3):

triangle(ABC, [A, B, C]):
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [0, R/3 + (2*R)/9]), (2*R)/9]):

center(C2), coordinates(center(C2)):

detail(C5):
circle(C6, [point(P5, [0, R/3 - (2*R)/9]), radius(C2)]):
circle(C7, [point(P7,[0, R/3 - (2*R)/9-(4*R)/9]), radius(C2)]):
circle(C8, [point(P8,[0, R/3 - (2*R)/9-(8*R)/9]), radius(C2)]):

circle(Cir, [point(Po, [0, -R/3 ]), (2*R)/3]):
draw([L1(color = blue),
ABC(color = red, transparency = 0.5, filled = true),
L2(color = blue), L3(color = blue),
C1(color = blue, thickness = 3),
C1(color = yellow, transparency = 0.8, filled = true),
C2(color = blue, filled = true),
C3(color = blue, filled = true),
C4(color = blue, filled = true),
C5(color = blue, filled = true),
C6(color = blue, filled = true),
C7(color = blue, filled = true),
C8(color = blue, filled = true),
Cir(color = red,transparency = 0.5,filled=true)],
axes = normal,
view = [-R .. R, -R .. R],
scaling = constrained);
I think a troucle with a symetry in respect to L2

## Sangatku...

I try differently
rotation(pol2,pol1,Pi/3,clockwise,o):
Error, (in geometry:-rotation) wrong type of arguments   Still that kind of error.

## Sangatku with equilateral triangle...

restart:
with(plots): with(geometry):
_EnvHorizontalName := 'x':
_EnvVerticalName := 'y':
a := 7:
point(E, 0, a*sqrt(3)/2):
point(B, -a/2, 0):
point(C, a/2, 0):
point(o, 0, a*sqrt(3)/6):
point(A, 0, a/2):
point(H, 0, 0):
R := (3-sqrt(3))*sqrt(2)*a/12:
point(J, 0, a*sqrt(3)/6 - R):
line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0):
reflection(J1, J, L1):coordJ1:=coordinates(J1):

line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0):
reflection(J2, J, L2):coordJ2:=coordinates(J2):
triangle(Tr1, [E, B, C]):
triangle(Tr2, [A, B, C]):
StretchRotation(E1, E, B, Pi/4, clockwise, sqrt(2)/2):
coordinates(E1):
StretchRotation(E2, E, C, Pi/4, counterclockwise, sqrt(2)/2):
coordinates(E2):
triangle(Tr3, [E, B, E1]):
triangle(Tr4, [E, C, E2]):
triangle(Tr5, [B, C, J]):
circle(cir, [point(P1,[0,a*sqrt(3)/6]), R]):
poly1 := Matrix( [ [0, a*sqrt(3)/2],
coordJ1,
[0, a/2],
coordJ2
],
datatype = float
):
pol1 := polygonplot(poly1, colour = green, transparency = 0.7, gridlines):
#poly2 := Matrix([ coordinates(J),coordinates(E1), coordJ2,|-a/2,0]],
datatype = float
):
#pol2 := polygonplot(poly2, colour = green, transparency = 0.7, gridlines):

tex := textplot([[0, a*sqrt(3)/2, "E"],[0,a*sqrt(3)/6 - R,"J"],
[-7/4 + (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4,"E1"],
[7/4 - (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4,"E2"],
[-7/4 + (((7*sqrt(3))/6 - 7*(3 - sqrt(3))*sqrt(2)/12)*sqrt(3))/2,
(7*sqrt(3))/6 + 7*(3 - sqrt(3))*   sqrt(2)/24,"J1"],
[7/4 - (((7*sqrt(3))/6 - 7*(3 - sqrt(3))*sqrt(2)/12)*sqrt(3))/2,
(7*sqrt(3))/6 + 7*(3 - sqrt(3))*   sqrt(2)/24,"J2"]], 'align' = {'above', 'right'}):
display( [ draw( [ Tr1(color = cyan),
Tr3(color = green),
cir(color=blue),
Tr2(color = red),
Tr4(color = grey),
Tr1(color=blue)],'view' = [-5 .. 5, 0 .. 7
],
axes = normal,
scaling = constrained,
size=[800,800]
),
tex
]
);

Error, `)` unexpected

line(L1, [B, o]):
Equation(L1):
line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0):
reflection(J1, J, L1):coordinates(J1):
triangle(Tr6, [B, J1, E]):
line(L2, [C, o]):
Equation(L2):
line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0):
reflection(J2, J, L2):coordinates(J2):
triangle(Tr7, [C, J2, E]):
triangle(T1, [E, J1, A]):
triangle(T2, [E, C, E2]):
triangle(T3, [B, H, J]):
triangle(T4, [C, H, J]):

display( [ draw( [ cir(color = orange, filled = true, transparency = 0.1),
Tr6(color = blue, filled = true, transparency = 0.2),
Tr5(color = blue, filled = true, transparency = 0.2),
Tr7(color = blue, filled = true, transparency = 0.2)

],
axes = none,
scaling = constrained
),
pol1
]
);
very difficult to find where I made mistakes; Thank you to help me.

## Coordinates of PP ?...

Ihave still errors.
restart:
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
b := a*(1/2 + 1/6*sqrt(45 - 24*sqrt(3)))^2:
r := b*sqrt(b)/(sqrt(a + b) + sqrt(a)):
assume(a > 0);
ellipse(E, x^2/a^2 + y^2/b^2 = 1):
circle(C3, [point(P3, [(1 + sqrt(3))*r, -r]), r]):
simplify(Equation(C3)):
sol:= solve( [Equation(C3), Equation(E), x>0, y<0]):
point(PP, [eval(x, sol), eval(y,sol)]):
simplify(coordinates(PP));

Warning, solve may be ignoring assumptions on the input variables.
Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received {x = ((3/13)*3^(1/2)*(15-8*3^(1/2))^(1/2)-(5/26)*3^(1/2)+(11/26)*(15-8*3^(1/2))^(1/2)+3/13)*a, y = -(1/4)*a*(4124*((3/13)*3^(1/2)*(15-8*3^(1/2))^(1/2)-(5/26)*3^(1/2)+(11/26)*(15-8*3^(1/2))^(1/2)+3/13)^4*3^(1/2)*(45-24*3^(1/2))^(1/2)+38376*((3/13)*3^(1/2)*(15-8*3^(1/2))^(1/2)-(5/26)*3^(1/2)+(11/26)*(15-8*3^(1/2))^(1/2)+3/13)^4*3^(1/2)+1476*((3/13)*3^(1/2)*(15-8*3^(1/2))^(1/2)-(5/26)*3^(1/2)+(11/26)*(15-8*3^(1/2))^(1/2)+3/13)^3*3^(1/2)*(45-24*3^(1/2))^(1/2)-7145*((3/13)*3^(1/2)*(15-8*3^(1/2))^(1/2)-(5/26)*3^(1/2)+(11/26)*(15-8*3^(1/2))^(1/2)+3/13)^4*(45-24*3^(1/2))^(1/2) ... 9/13)*(15-8*3^(1/2))^(1/2)+70542/13+426*(45-24*3^(1/2))^(1/2)), 0 < a}
Error, (in geometry:-coordinates) wrong type of argument

## Sangatku...

I am trying to know the coordinates of PP with a and b parameters
p and q are the lengths of the horizontal and vertical sides of the triangle T1
more I know that : xPP=a-2*a*p*(b-q)./(2*a*b-p*q): that  yPP=b-2*b*q*(a-p)./(2*a*b-p*q):and that 2*(a-p)*(b-q)=p*q)
Program attempt :
restart:
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
b := a*(1/2 + 1/6*sqrt(45 - 24*sqrt(3)))^2:
r := b*sqrt(b)/(sqrt(a + b) + sqrt(a)):
ellipse(E, x^2/a^2 + y^2/b^2 = 1):
circle(C3, [point(P3, [(1 + sqrt(3))*r, -r]), r]):
Equation(C3);

ellipse: hint: unable to determine if 1/a^4/(1/2+1/6*(45-24*3^(1/2))^(1/2))^4 is zero
Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse
circle: hint: a^(3/2)*(1/2+1/6*(45-24*3^(1/2))^(1/2))^3/((a+a*(1/2+1/6*(45-24*3^(1/2))^(1/2))^2)^(1/2)+a^(1/2)) > 0
Error, (in geometry:-circle) not enough information: the radius might not be positive
Error, (in geometry:-Equation) wrong type of argument
NULL;
Is it possible to find the coordinates of PP with a and b as parameters. Thank you very much.

## Sangatku...

Best reagards. Can you tell me why :IsOnCircle(PP, ic1); gives false.

## Sangaku...

restart;
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:

a := 7:
b := a*(1/2 + 1/6*sqrt(45 - 24*sqrt(3)))^2:
r := b*sqrt(b)/(sqrt(a + b) + sqrt(a)):
Tt := [5.349255162, 2.829908743]:
eq := x*Tt[1]/a^2 + y*Tt[2]/b^2 = 1:
subs(y = b, eq):
Pp := [solve(%, x), b]:
subs(x = a, eq):
Qq := [a, solve(%)]:
point(P, Pp[1], Pp[2]):
point(Q, Qq[1], Qq[2]):

point(A, -a, -b):
point(B, -a, b):
point(C, a, b):
point(F, a, -b):
point(T, [5.349255162, 2.829908743]):
square(Sq, [A, B, C, F]):
line(Lig,x=0):
line(Liq,y=0):
triangle(PQC,[P,Q,C]):
incircle(Cir1, PQC, 'centername' = o):
circle(C1, [point(P1, [r, 0]), r]):
circle(C2, [point(P2, [(1 + sqrt(3))*r, r]), r]):
circle(C3, [point(P3, [(1 + sqrt(3))*r, -r]), r]):
ellipse(E, x^2/a^2 + y^2/b^2 = 1, [x, y]):
fsolve( {Equation(C1), x^2/a^2 + y^2/b^2 = 1}, complex):
reflection(C4, C1, Lig):
reflection(C5, C2, Lig):
reflection(C6, C3, Lig):
reflection(Cir2, Cir1, Lig):
reflection(Cir3,Cir1,Liq):
reflection(Cir4,Cir2,Liq):
draw( [ Sq(color = blue,filled=true,thickness=4,transparency=0.7),
C1(color = orange, filled = true,transparency=0.7),
E(color=white,thickness=4),
C2(color = orange, filled = true,transparency=0.7),
C3(color = orange, filled = true,transparency=0.7),
C4(color = orange, filled = true,transparency=0.7),
C5(color = orange, filled = true,transparency=0.7),
C6(color = orange, filled = true,transparency=0.7),
Cir1(color = red, filled = true,transparency=0.5),
Cir2(color = red, filled = true,transparency=0.5),
Cir3(color = red, filled = true,transparency=0.5),
Cir4(color = red, filled = true,transparency=0.5),

Sq(color=blue)
],
axes = none,
view = [-a .. a, -b .. b],
scaling = constrained
);The coordinates of T are approximate; Can be done better.Choose colors with RGB.Thank you.

## coordinates of the center of the circle ...

Cen := proc(M, N, R) local eq1, eq2, sol;
eq1 := EqBIS(M, N, R) = 0;
eq2 := EqBIS(N, M, R) = 0;
sol := simplify(solve({eq1, eq2}, {x, y}));
RETURN([subs(sol, x), subs(sol, y)]);
end proc
Ce := Cen(P, Dd, Q);
Error, (in LinearAlgebra:-Norm) expects its 1st argument, A, to be of type {Matrix, Vector}, but received [-5, 0]

Why have I this message ?     Thank youi.

## Other programma...

restat;
with(plots);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
a := 11;
b := 5;
NULL;
fig := proc(theta) local aa, bb, ell, Ell, m, p, sol, A, B, C, Dd, quadri; global a, b; ell := (x*cos(theta) + y*sin(theta))^2/a^2 + (x*sin(theta) - y*cos(theta))^2/b^2 = 1; sol := solve({y = m, ell}, {x, y}, explicit); subs(sol[1], x) = subs(sol[2], x); sol := solve(%, m); bb := sol[1]; sol := solve({x = p, ell}, {x, y}, explicit); subs(sol[1], y) = subs(sol[2], y); sol := solve(%, p); aa := sol[1]; A := [aa, bb]; B := [aa, -bb]; C := [-aa, -bb]; Dd := [-aa, bb]; Ell := implicitplot(ell, x = -12 .. 12, y = -12 .. 12, thickness = 3, color = blue); quadri := plot([A, B, C, Dd, A], color = pink, filled = true); display([quadri, Ell], scaling = constrained, axes = none); end proc;
nframes := 10:
frames := seq(fig(2*Pi*i/(2*nframes)), i=0..nframes-1):
display(frames, insequence);

Thank you for your last programma. Here is mine who needs to be improved.

## Rectangle and ellipse...

Apart from the animation, I consider that your program is more complicated than mine. Would you have an animation without Geometry ?

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﻿